"The art of counting and recording number is one of the oldest mathematical skills for which we have evidence. In fact, there is some evidence that it preceded a written language" (Wall, pg. 11).
The invention of numbers was thought to have start many thousands of years ago, and used in as a one to one correspondence to keep track of quantity of livestock other valuable possessions. As the demand for numbers became more necessary, people started creating systems that symbolized quantities, moving numbers from their physical properties to their abstract properties. Still, these values were used to keep record of livestock, property, and trade. For this reason, numbers were initially only whole numbers and perhaps rational numbers.
As numbers became a more practical part of life, civilizations began to work with them. The Babylonians began testing claims and were one of the first people to develop a system of taking the square root. The Greeks began looking at geometric structures. As math evolved to become more abstract, ideas became more complex and popular. None of these more complex notions would even be rational or valid without the invention of numbers. So, let's take a trip down memory lane and review some of the early ways of counting.
Tally Stick
Used most likely with the one-to-one correspondence system, the tally stick used marks to denote numbers. It was probably one of the first numeric representation systems.
A Tally Stick. Notice that an X is used to represent 10
How tally sticks were possibly made.
Egyptian Recording System
One of the earliest recording systems was the Egyptian recording systems. Using Egyptian hieroglyphics, this civilization's system rounded of at decimal numbers and did not have a way to record irrational numbers. Their system was a base 10 system, like our system today. Below, you will find the hieroglyphics that correspond with the numbers.
Egyptian numerials. Below, you will find the values for each of the symbols.
Strike: Used for numerals 1 - 9. Each strike symbolized a number 1-9. Thus, 5 would look like this: ||| || Heel Bone: Used to represent collections of 10. Coil of Rope: Used to represent collections of 100. Water Lilly: Used to represent collections of 1,000. Bent Finger: Used to represent collections of 10,000. Tadpole: Used to represent collections of 100,000. Astonished Man: Used to represent collections of 1,000,000.
The Roman System
The Roman system as been used is thought to have been in use as early as 800BC. It is a decimal system, but not necessarily positional, for there is no value representing the number zero. After the fall of the Roman Empire, Roman Numerals were widely abandoned and replaced with the Arabic system that we use today. Below is an index of Roman Numerals:
I II V X L C D M 1 2 5 10 50 100 500 1000 Roman Numerals Want to convert any number to Roman fast? Click here! (The converter is the purple box on the right-hand side of the page!)
Attic Greek Numerals
Attic Greek numerals were thought to have been used as early as 700 AD and are similar to the Roman numeral system. This is a simple grouping system. The numerals can be found below:
Attic Greek numerals.
Chinese - Japanese System
The Chinese-Japanese system is also a multiplicative grouping system where numbers are written vertically:
Other Systems
There are other systems that can be used, but not all can be demonstrated here. Other systems are the Greek Alphabetic system which uses 27 symbols to represent numbers 1-9, 10-90, and 100-900. To learn more about the Greek Alphabetic system, click here. The Gorbar Arabic system is one that closely resembles the numerals that we use today. See page 14 in Number Theory to view these numbers.
"The art of counting and recording number is one of the oldest mathematical skills for which we have evidence. In fact, there is some evidence that it preceded a written language" (Wall, pg. 11).
Table of Contents
The invention of numbers was thought to have start many thousands of years ago, and used in as a one to one correspondence to keep track of quantity of livestock other valuable possessions. As the demand for numbers became more necessary, people started creating systems that symbolized quantities, moving numbers from their physical properties to their abstract properties. Still, these values were used to keep record of livestock, property, and trade. For this reason, numbers were initially only whole numbers and perhaps rational numbers.
As numbers became a more practical part of life, civilizations began to work with them. The Babylonians began testing claims and were one of the first people to develop a system of taking the square root. The Greeks began looking at geometric structures. As math evolved to become more abstract, ideas became more complex and popular. None of these more complex notions would even be rational or valid without the invention of numbers. So, let's take a trip down memory lane and review some of the early ways of counting.
Tally Stick
Used most likely with the one-to-one correspondence system, the tally stick used marks to denote numbers. It was probably one of the first numeric representation systems.Egyptian Recording System
One of the earliest recording systems was the Egyptian recording systems. Using Egyptian hieroglyphics, this civilization's system rounded of at decimal numbers and did not have a way to record irrational numbers. Their system was a base 10 system, like our system today. Below, you will find the hieroglyphics that correspond with the numbers.Strike: Used for numerals 1 - 9. Each strike symbolized a number 1-9. Thus, 5 would look like this:
|||
||
Heel Bone: Used to represent collections of 10.
Coil of Rope: Used to represent collections of 100.
Water Lilly: Used to represent collections of 1,000.
Bent Finger: Used to represent collections of 10,000.
Tadpole: Used to represent collections of 100,000.
Astonished Man: Used to represent collections of 1,000,000.
The Roman System
The Roman system as been used is thought to have been in use as early as 800BC. It is a decimal system, but not necessarily positional, for there is no value representing the number zero. After the fall of the Roman Empire, Roman Numerals were widely abandoned and replaced with the Arabic system that we use today. Below is an index of Roman Numerals:I II V X L C D M
1 2 5 10 50 100 500 1000
Roman Numerals
Want to convert any number to Roman fast? Click here!
(The converter is the purple box on the right-hand side of the page!)
Attic Greek Numerals
Attic Greek numerals were thought to have been used as early as 700 AD and are similar to the Roman numeral system. This is a simple grouping system. The numerals can be found below:Chinese - Japanese System
The Chinese-Japanese system is also a multiplicative grouping system where numbers are written vertically:Other Systems
There are other systems that can be used, but not all can be demonstrated here. Other systems are the Greek Alphabetic system which uses 27 symbols to represent numbers 1-9, 10-90, and 100-900. To learn more about the Greek Alphabetic system, click here. The Gorbar Arabic system is one that closely resembles the numerals that we use today. See page 14 in Number Theory to view these numbers.Sources:
Creative Commons. (Designer). (2008). 500 attic greek. [Print Photo]. Retrieved from http://commons.wikimedia.org/wiki/Category:Greek_numeral
Deacon, S. (Designer). (2010). Chinese-japanese numbers. [Web Photo]. Retrieved from http://www.importanceoflanguages.com/LearnJapanese/rocket-japanese/
Forex, J. (Designer). (2011). Tally Sticks. [Web Photo]. Retrieved from http://falconlog.blogspot.com/2011/02/modern-money-mechanics-work-in-progress.html
Gleason, D. (Designer). (2008). Attic greek numerals. [Print Photo]. Retrieved from http://www.jesus8880.com/chapters/gematria/greek-numerals.htm
Wall, E. (2010). Number theory for elementary school teachers . Boston: McGraw Hill Higher Education.
Yanze, D. (Photographer). (2009). Egyptian number system. [Web Photo]. Retrieved from http://ancientegypt3.blogspot.com/2009/06/egyptian-numeration.html